D anika H aym an Department of Bioengineering, Imperial College of London, South Kensington Campus, London S W 7 2AZ, UK e-m ail: danika.hayman@ imperial.ac.uk
C hristie Bergerson Department of Biomedical Engineering, Texas A & M , College Station, TX 77843 e-m ail: cmbergerson@ gm ail.com
S am an th a M ille r Department of Biomedical Engineering, Texas A & M , College Station, TX 77843
M ic h a e l M oreno Department of Biomedical Engineering, Texas A & M , College Station, TX 77843 e-m ail: m m oreno@ bm e.tam u.edu
Ja m e s E. M o o re 1 Department of Bioengineering, Imperial College of London, South Kensington Campus, London S W 7 2AZ, UK e-m ail: james.m oore.jr@ im perial.ac.uk
The Effect of Static and Dynamic Loading on Degradation of PLLA Stent Fibers Understanding how polymers such as PLLA degrade in vivo will enhance biodegradable stent design. This study examined the effect of static and dynamic loads on PLLA stent fibers in vitro. The stent fibers (generously provided by TissueGen, Inc.) were loaded axi ally with ON, 0.5N, 1N, or 0.125-0.25N (dynamic group, 1 Hz) and degraded in PBS at 45 °C for an equivalent degradation time of 15 months. Degradation was quantified through changes in tensile mechanical properties. The mechanical behavior was charac terized using the Knowles strain energy function and a degradation model. A nonsignifi cant increase in fiber stiffness was observed between 0 and 6 months followed by fiber softening thereafter. A marker of fiber softening, [1, increased between 9 and 15 months in all groups. At 15 months, the ft values in the dynamic group were significantly higher compared to the other groups. In addition, the model indicated that the degradation rate constant was smaller in the 1-N (0.257) and dynamic (0.283) groups compared to the 0.5-N (0.516) and 0-N (0.406) groups. While the shear modulus fluctuated throughout degradation, no significant differences were observed. Our results indicate that an increase in static load increased the degradation of mechanical properties and that the application o f dynamic load further accelerated this degradation. [DOI: 10.1115/1.4027614]
Introduction The transient nature of biodegradable stents may decrease long term complications associated with traditional stents such as restenosis and incomplete re-endothelialization [1], However, designing biodegradable stents that can maintain their mechanical integrity throughout the degradation process presents a new set of challenges. Poly-L-lactic acid (PLLA), a nontoxic polymer that is easily eliminated from the body, is often used in degradable devices. Clinical studies of PLLA stents such as the Igaki-Tamai stent and the BVS stent (Abbott Vascular) indicate that, although the stents are safe, they are prone to greater elastic recoil compared to bare metal stents [2-5], Attempts to correct this problem are addressed through changes in stent design. Currently, a second-generation BVS stent is undergoing clinical trials (ClinicalTrials.gov; NCT01425281), and additional designs are under investigation in animal models and in vitro [6-12], However, the design process is complicated by an incomplete understanding of how the PLLA degradation rate is impacted by its local mechanical environment. PLLA has been used in a variety of medical devices and con sumer products; so much is known about the effect of material and environmental properties on its degradation rate. The primary degradation mechanism of PLLA is passive hydrolysis of the ester bond [13]; however, enzymatic degradation can also occur [14], The degradation rate and erosion mechanism are affected by changes in characteristic material properties such as percent crys tallinity [15] and geometry [16] or environmental factors such as pH [17], water uptake [18], and temperature [19], Given this in formation, it is possible to predict how changes in material proper ties or environment will alter the degradation rate [20], However, 'Corresponding author. Manuscript received November 14, 2013; final manuscript received April 11, 2014; accepted manuscript posted May 8, 2014; published online June 3, 2014. Assoc. Editor: Sean S. Kohles.
Journal of Biomechanical Engineering
very little is known about the effect of loading on the degradation rate as most in vitro degradation studies are performed in the ab sence of mechanical loads. In vivo studies of biodegradable devices suggest that loading accelerates degradation in polymers. Specifically, the degradation rates are higher in devices experiencing high compressive load such as spinal cages, bone screws, and bone plates compared to unloaded in vitro controls [21,22], However, it is difficult to extrapolate these results to stent design as these loads are not com parable to those found in stents, the degradation rates have not been quantified, the changes in mechanical properties have not been well characterized, and the complex loading conditions in vivo make it difficult or impossible to quantify the relationship between load and degradation rate [21,23], In vitro studies offer more quantifiable results; however, few degradation studies have been carried out under loaded condi tions. One study that examined the effects of a tensile load and a dynamic tensile load on poly-D,L-lactic acid (PDLLA) foams found that both increased the degradation rate and decreased the molecular weight, elastic modulus, and tensile strength after 3 months [24]. Other studies of PLLA foams, composites, and copolymers have also found an increase in degradation with load through a decrease in mechanical properties [25,26]. In one study of dynamically compressed 50:50 PLA:PGA implants dynamic loading significantly increased material stiffness during the first 3 weeks [26]. These studies all indicate that load affects degradation rate; however, the polymer geometries and composition are too variable to compare between studies or define a quantitative rela tionship [27]. Conversely, a study on the degradation of poly(glycolide-co-Llactide) (PGLA) sutures suggests that smaller loads may have less effect on degradation. When a static load of less than 1 N was applied to braided sutures, no change was seen in the breaking strength retention, tensile modulus retention, or tensile breaking strain [28], These loads are much smaller than those described in
Copyright © 2014 by ASME
AUGUST 2014, Vol. 136 / 081006-1
the above studies, which suggests there may be a critical loading value below which the change in degradation is less pronounced. A rapid decrease in elastic modulus was observed within the first 5 days of degradation; this was followed by a 20-day period of elastic modulus stability. The authors attribute this initial decrease in elastic modulus to the plasticizing effect of water absorption in the PLLA sutures [18,28]. Despite the paucity of experimental data, material models have been developed, which predict degradation based on thermody namic factors. Rajagopal et al. developed a model of polymer deg radation as a function of deformation measured by the first strain invariant [29], In this model, degradation is driven by strain alone so that, in the unloaded model, the degradation rate is zero. Degra dation is introduced to the neo-Hookean material model through a deformation dependent decrease in the shear modulus. Soares et al. further developed this model for use with PLLA stent fibers under tensile loading conditions [30-33]. The degradation model was applied with a neo-Hookean constitutive description to fibers loaded under uniaxial extension [32]. In this model, the degrada tion rate is a function of deformation, which is quantified by the radius in the (IB, IIB) plane. When the degradation model was applied to more complex strain energy functions, a better descrip tion of the mechanical behavior was obtained. The Knowles strain energy function, which provided a good description of PLLA behavior, was allowed to degrade through a decrease in the three characteristic material parameters [30]. The Knowles model was chosen over the traditionally used Young’s modulus because semicrystalline polymers such as PLLA exhibit nonlinear behav ior, which extends to several percent strain. While the Young’s modulus can provide a description of overall material behavior for small strains (
20 -
0
^
•fifi*’
.}*' -■ w
#
20
»!••*'
iM 1' -
0 2
4
6
g
0
2
undegraded
■ 6 m onths
4
6
strain [%]
strain [%]
9 m onths
« 12 m onths
• 15 m onths
F ig . 2 A v e r a g e s tr e s s v e r s u s s tr a in c u r v e s f o r t h e e la s t ic r e g io n s o f f ib e r s e x p o s e d t o (a ) d y n a m ic lo a d , ( b ) n o lo a d , (c ) s m a ll s t a t ic lo a d , a n d ( d ) la r g e s t a t ic lo a d a t 0 , 6 , 9 , 1 2 , a n d 1 5 m o n th s
T a b le 1
A v e r a g e v a lu e s f o r t h e K n o w le s m o d e l m a te r ia l c o n s t a n t s f o r a ll s t a t ic ( n = 2 ) a n d d y n a m ic ( n = 3 ) lo a d in g g r o u p s
t=
No load (ON)
0 months
6 months
9 months
612.5 ± 30.6 MPa (n = 4); 461.6 (n = l); 663.2 ±1.0; 30.7 ± 4.0 1.8; 35.0 ± 0.4; (dimensionless); 6.6 x 10~3 5.9 x 10-5 ± 3.5 x m = 8.1 x 10~5 ± 1.3 x 10”6 Small static (dimensionless) 456.0 (n = l); 591.2 ±6.7; load (0.5 N) 0.9; 32.8 ± 3.8; 4.2 x 10“2 6.8 x 10^5 ± 5.8 x Large static 535.9 ± 34.0; 567.0 ± 80.7; load (IN ) 12.9 ± 6.3; 27.7 ± 5.8; 6.8 x 10-5 ± 3.0 x 10“5 7.4 x 10“5 ± 7.2 x Dynamic load 549.5 ± 38.6; 583.5 ±112.6; 10.1 ±3.4; (0.125-0.25N, 31.2 ± 15.3; 1 Hz) 6.5 x 10-4 ± 4.5 x 10-4 6.9 x 10-5 ± 2.4 x
F ig . 3
ft = P=
Illu s tr a tio n o f t h e e ffe c t o f v a r y in g /i w h ile k e e p in g p a n d
m c o n s ta n t. A n in c r e a s e in /I in d ic a te s a s o fte r m a te r ia l a t h ig h e r s tr a in s .
081006-4 / Vol. 136, AUGUST 2014
12 months
15 months
715.6 ±7.6; 52.6 ± 4.5;
636.3 ± 133.8; 62.2 ±44.5; 5.7 x 10~5 ± 1.8 x 10"5
10-6 4.1 x 10“5± 1.9 x 732.7 ± 24.3; 51.0 ±6.0; 10“6 4.3 x 10“5 ± 3.8 x 706.8 ± 17.3; 44.3 ± 8.6; 10~6 6.4 x 10_s ± 1.5 x 550.8 ± 49.6; 34.8 ± 5.6; 10~5 7.2 x 10"5 ± 1.2 x
10“6 614.7 ± 19.7; 88.5 ± 33.4; 10~6 6.7 x 10“5 ± 8.3 x 10“6 611.9 (n = 1); 140.1; 10~5 7.7 x 10“5 594.5 ± 69.0; 133.9 ± 1.7; 10“5 9.6 x 10-5 ± 4.4 x 10“5
static load group where values ranged from 12.9 to 140.1. This change resulted in roughly half the predicted stress at a strain of 5% when ft and m are held constant. The M l degradation model indicated an increase in degradation rate through an increase in Kp (Eq. (5)) with increasing static load (Table 2). Kp also increased in the dynamic load group. However, while the M l model was able to generally describe the observed increase in /?, there was significant error in the predicted values (Fig. 5). The M2 model predicted fi values with less error. Because o f the differing values o f ft0 at 6 months, the values o f Kp obtained from the M 2 m odel did not follow the same trend. In this case the value of Kp decreased with an increase in the value o f /?0. In addition, the distinct confidence intervals in this case indicated that the Kp values for the large static load and dynamic load groups were significantly smaller than the Kp value obtained for the small static load group. W hen the relationship between degra dation load and Kp was examined for m odel M2, a linear relation ship was observed in the data (Fig. 6). Kp decreased with increased degradation stress in the statically loaded groups. The Kp value for the dynamic load group was not included in the linear fit. Transactions of the ASME
160
#
effective degradation time [months] Q n o lo a d (ON)
£■ s m a ll s ta tic lo a d (0 .5 N )
□ la rg e s ta tic lo a d ( I N )
a d y n a m ic lo a d (0 .1 2 5 -0 .2 5 N , 1Hz)
Fig. 4 p,a Knowles model constant, increases with degradation time. *p
C hristie Bergerson Department of Biomedical Engineering, Texas A & M , College Station, TX 77843 e-m ail: cmbergerson@ gm ail.com
S am an th a M ille r Department of Biomedical Engineering, Texas A & M , College Station, TX 77843
M ic h a e l M oreno Department of Biomedical Engineering, Texas A & M , College Station, TX 77843 e-m ail: m m oreno@ bm e.tam u.edu
Ja m e s E. M o o re 1 Department of Bioengineering, Imperial College of London, South Kensington Campus, London S W 7 2AZ, UK e-m ail: james.m oore.jr@ im perial.ac.uk
The Effect of Static and Dynamic Loading on Degradation of PLLA Stent Fibers Understanding how polymers such as PLLA degrade in vivo will enhance biodegradable stent design. This study examined the effect of static and dynamic loads on PLLA stent fibers in vitro. The stent fibers (generously provided by TissueGen, Inc.) were loaded axi ally with ON, 0.5N, 1N, or 0.125-0.25N (dynamic group, 1 Hz) and degraded in PBS at 45 °C for an equivalent degradation time of 15 months. Degradation was quantified through changes in tensile mechanical properties. The mechanical behavior was charac terized using the Knowles strain energy function and a degradation model. A nonsignifi cant increase in fiber stiffness was observed between 0 and 6 months followed by fiber softening thereafter. A marker of fiber softening, [1, increased between 9 and 15 months in all groups. At 15 months, the ft values in the dynamic group were significantly higher compared to the other groups. In addition, the model indicated that the degradation rate constant was smaller in the 1-N (0.257) and dynamic (0.283) groups compared to the 0.5-N (0.516) and 0-N (0.406) groups. While the shear modulus fluctuated throughout degradation, no significant differences were observed. Our results indicate that an increase in static load increased the degradation of mechanical properties and that the application o f dynamic load further accelerated this degradation. [DOI: 10.1115/1.4027614]
Introduction The transient nature of biodegradable stents may decrease long term complications associated with traditional stents such as restenosis and incomplete re-endothelialization [1], However, designing biodegradable stents that can maintain their mechanical integrity throughout the degradation process presents a new set of challenges. Poly-L-lactic acid (PLLA), a nontoxic polymer that is easily eliminated from the body, is often used in degradable devices. Clinical studies of PLLA stents such as the Igaki-Tamai stent and the BVS stent (Abbott Vascular) indicate that, although the stents are safe, they are prone to greater elastic recoil compared to bare metal stents [2-5], Attempts to correct this problem are addressed through changes in stent design. Currently, a second-generation BVS stent is undergoing clinical trials (ClinicalTrials.gov; NCT01425281), and additional designs are under investigation in animal models and in vitro [6-12], However, the design process is complicated by an incomplete understanding of how the PLLA degradation rate is impacted by its local mechanical environment. PLLA has been used in a variety of medical devices and con sumer products; so much is known about the effect of material and environmental properties on its degradation rate. The primary degradation mechanism of PLLA is passive hydrolysis of the ester bond [13]; however, enzymatic degradation can also occur [14], The degradation rate and erosion mechanism are affected by changes in characteristic material properties such as percent crys tallinity [15] and geometry [16] or environmental factors such as pH [17], water uptake [18], and temperature [19], Given this in formation, it is possible to predict how changes in material proper ties or environment will alter the degradation rate [20], However, 'Corresponding author. Manuscript received November 14, 2013; final manuscript received April 11, 2014; accepted manuscript posted May 8, 2014; published online June 3, 2014. Assoc. Editor: Sean S. Kohles.
Journal of Biomechanical Engineering
very little is known about the effect of loading on the degradation rate as most in vitro degradation studies are performed in the ab sence of mechanical loads. In vivo studies of biodegradable devices suggest that loading accelerates degradation in polymers. Specifically, the degradation rates are higher in devices experiencing high compressive load such as spinal cages, bone screws, and bone plates compared to unloaded in vitro controls [21,22], However, it is difficult to extrapolate these results to stent design as these loads are not com parable to those found in stents, the degradation rates have not been quantified, the changes in mechanical properties have not been well characterized, and the complex loading conditions in vivo make it difficult or impossible to quantify the relationship between load and degradation rate [21,23], In vitro studies offer more quantifiable results; however, few degradation studies have been carried out under loaded condi tions. One study that examined the effects of a tensile load and a dynamic tensile load on poly-D,L-lactic acid (PDLLA) foams found that both increased the degradation rate and decreased the molecular weight, elastic modulus, and tensile strength after 3 months [24]. Other studies of PLLA foams, composites, and copolymers have also found an increase in degradation with load through a decrease in mechanical properties [25,26]. In one study of dynamically compressed 50:50 PLA:PGA implants dynamic loading significantly increased material stiffness during the first 3 weeks [26]. These studies all indicate that load affects degradation rate; however, the polymer geometries and composition are too variable to compare between studies or define a quantitative rela tionship [27]. Conversely, a study on the degradation of poly(glycolide-co-Llactide) (PGLA) sutures suggests that smaller loads may have less effect on degradation. When a static load of less than 1 N was applied to braided sutures, no change was seen in the breaking strength retention, tensile modulus retention, or tensile breaking strain [28], These loads are much smaller than those described in
Copyright © 2014 by ASME
AUGUST 2014, Vol. 136 / 081006-1
the above studies, which suggests there may be a critical loading value below which the change in degradation is less pronounced. A rapid decrease in elastic modulus was observed within the first 5 days of degradation; this was followed by a 20-day period of elastic modulus stability. The authors attribute this initial decrease in elastic modulus to the plasticizing effect of water absorption in the PLLA sutures [18,28]. Despite the paucity of experimental data, material models have been developed, which predict degradation based on thermody namic factors. Rajagopal et al. developed a model of polymer deg radation as a function of deformation measured by the first strain invariant [29], In this model, degradation is driven by strain alone so that, in the unloaded model, the degradation rate is zero. Degra dation is introduced to the neo-Hookean material model through a deformation dependent decrease in the shear modulus. Soares et al. further developed this model for use with PLLA stent fibers under tensile loading conditions [30-33]. The degradation model was applied with a neo-Hookean constitutive description to fibers loaded under uniaxial extension [32]. In this model, the degrada tion rate is a function of deformation, which is quantified by the radius in the (IB, IIB) plane. When the degradation model was applied to more complex strain energy functions, a better descrip tion of the mechanical behavior was obtained. The Knowles strain energy function, which provided a good description of PLLA behavior, was allowed to degrade through a decrease in the three characteristic material parameters [30]. The Knowles model was chosen over the traditionally used Young’s modulus because semicrystalline polymers such as PLLA exhibit nonlinear behav ior, which extends to several percent strain. While the Young’s modulus can provide a description of overall material behavior for small strains (
20 -
0
^
•fifi*’
.}*' -■ w
#
20
»!••*'
iM 1' -
0 2
4
6
g
0
2
undegraded
■ 6 m onths
4
6
strain [%]
strain [%]
9 m onths
« 12 m onths
• 15 m onths
F ig . 2 A v e r a g e s tr e s s v e r s u s s tr a in c u r v e s f o r t h e e la s t ic r e g io n s o f f ib e r s e x p o s e d t o (a ) d y n a m ic lo a d , ( b ) n o lo a d , (c ) s m a ll s t a t ic lo a d , a n d ( d ) la r g e s t a t ic lo a d a t 0 , 6 , 9 , 1 2 , a n d 1 5 m o n th s
T a b le 1
A v e r a g e v a lu e s f o r t h e K n o w le s m o d e l m a te r ia l c o n s t a n t s f o r a ll s t a t ic ( n = 2 ) a n d d y n a m ic ( n = 3 ) lo a d in g g r o u p s
t=
No load (ON)
0 months
6 months
9 months
612.5 ± 30.6 MPa (n = 4); 461.6 (n = l); 663.2 ±1.0; 30.7 ± 4.0 1.8; 35.0 ± 0.4; (dimensionless); 6.6 x 10~3 5.9 x 10-5 ± 3.5 x m = 8.1 x 10~5 ± 1.3 x 10”6 Small static (dimensionless) 456.0 (n = l); 591.2 ±6.7; load (0.5 N) 0.9; 32.8 ± 3.8; 4.2 x 10“2 6.8 x 10^5 ± 5.8 x Large static 535.9 ± 34.0; 567.0 ± 80.7; load (IN ) 12.9 ± 6.3; 27.7 ± 5.8; 6.8 x 10-5 ± 3.0 x 10“5 7.4 x 10“5 ± 7.2 x Dynamic load 549.5 ± 38.6; 583.5 ±112.6; 10.1 ±3.4; (0.125-0.25N, 31.2 ± 15.3; 1 Hz) 6.5 x 10-4 ± 4.5 x 10-4 6.9 x 10-5 ± 2.4 x
F ig . 3
ft = P=
Illu s tr a tio n o f t h e e ffe c t o f v a r y in g /i w h ile k e e p in g p a n d
m c o n s ta n t. A n in c r e a s e in /I in d ic a te s a s o fte r m a te r ia l a t h ig h e r s tr a in s .
081006-4 / Vol. 136, AUGUST 2014
12 months
15 months
715.6 ±7.6; 52.6 ± 4.5;
636.3 ± 133.8; 62.2 ±44.5; 5.7 x 10~5 ± 1.8 x 10"5
10-6 4.1 x 10“5± 1.9 x 732.7 ± 24.3; 51.0 ±6.0; 10“6 4.3 x 10“5 ± 3.8 x 706.8 ± 17.3; 44.3 ± 8.6; 10~6 6.4 x 10_s ± 1.5 x 550.8 ± 49.6; 34.8 ± 5.6; 10~5 7.2 x 10"5 ± 1.2 x
10“6 614.7 ± 19.7; 88.5 ± 33.4; 10~6 6.7 x 10“5 ± 8.3 x 10“6 611.9 (n = 1); 140.1; 10~5 7.7 x 10“5 594.5 ± 69.0; 133.9 ± 1.7; 10“5 9.6 x 10-5 ± 4.4 x 10“5
static load group where values ranged from 12.9 to 140.1. This change resulted in roughly half the predicted stress at a strain of 5% when ft and m are held constant. The M l degradation model indicated an increase in degradation rate through an increase in Kp (Eq. (5)) with increasing static load (Table 2). Kp also increased in the dynamic load group. However, while the M l model was able to generally describe the observed increase in /?, there was significant error in the predicted values (Fig. 5). The M2 model predicted fi values with less error. Because o f the differing values o f ft0 at 6 months, the values o f Kp obtained from the M 2 m odel did not follow the same trend. In this case the value of Kp decreased with an increase in the value o f /?0. In addition, the distinct confidence intervals in this case indicated that the Kp values for the large static load and dynamic load groups were significantly smaller than the Kp value obtained for the small static load group. W hen the relationship between degra dation load and Kp was examined for m odel M2, a linear relation ship was observed in the data (Fig. 6). Kp decreased with increased degradation stress in the statically loaded groups. The Kp value for the dynamic load group was not included in the linear fit. Transactions of the ASME
160
#
effective degradation time [months] Q n o lo a d (ON)
£■ s m a ll s ta tic lo a d (0 .5 N )
□ la rg e s ta tic lo a d ( I N )
a d y n a m ic lo a d (0 .1 2 5 -0 .2 5 N , 1Hz)
Fig. 4 p,a Knowles model constant, increases with degradation time. *p
